Question

Let M1, M2 and M3 are linearly independent sets of vectors, and that M, C M, CM2. Let M = M, UM, U M3. Then, which of the following is always true? a) M is linearly dependent b) M is linearly independent c) M is both linearly dependent and linearly independent d) M is neither linearly dependent nor linearly independent

Answer 1

(b) option true

Let & M3 м., м., м are 80 Solution Mi = {1} M2 = {1, 2} M3 = {1, rin} clearly M, CM2 CM3 and lineady réndependent set M = MUM U Mz = {13 U{1,2} Ud{1,2,3%} M = { 1, x.x2y = M2 Because M es linear (a) False, linear linealy independent m is not tineady dependeort eineady independent (6) True. Because of ACBCC ( False, Because M is Because (d) Folse, then AUBUC SC M, & M₂, & M3 are lin lineady independent & M = MIU Mg UM₂ M = M₂ M és also lineady lineady independent, independent. {i: My 8